1+tan² A\1+cot²A=[1-tanA\1-cotA]²=tan²A
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LHS:
= 1+tan²A / 1+cot²A
= Sec²A/ Cosec²A
= Sin²A/Cos²A
= tan²A
RHS:
=(1-tanA)²/(1-cotA)²
=(1-sinA/cosA)²/(1-cosA/sinA)²
=[(cosA-sinA)/cosA]²
/ [(sinA-cos)/sinA)²
=(cosA-sinA)²×sin²A
/Cos²A. /(sinA-cosA)²
=1×sin²A
/Cos²A×1. ?? (-1)²= 1
=tan²A
Hence proved
Let me know if there are some corrections...Thanks!
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